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Index And Stability In Bimatrix Games


Index And Stability In Bimatrix Games
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Index And Stability In Bimatrix Games


Index And Stability In Bimatrix Games
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Author : H. Arndt von Schemde
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-11

Index And Stability In Bimatrix Games written by H. Arndt von Schemde and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-11 with Business & Economics categories.


The index of an equilibrium in a game gives information about the "stability" of the equilibrium, for example with respect to game dynamics. Unfortunately, index theory is often very technical. This book presents a new geometric construction that visualises the index in an intuitive way. For example, a 3A-n game, for any n, can be represented by a figure in the plane, from which one can read off any equilibrium, and its index as a geometric orientation. With this insight, the index can be characterised in strategic terms alone. Moreover, certain "hyperstable" equilibrium components are seen to have nonzero index. The construction gives an elementary proof that two-player games have a Nash equilibrium, and, in an unusual direction, the powerful fixed point theorem of Brouwer.



Index And Stability In Bimatrix Games


Index And Stability In Bimatrix Games
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Author : H. Arndt von Schemde
language : en
Publisher: Springer
Release Date : 2005-08-22

Index And Stability In Bimatrix Games written by H. Arndt von Schemde and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-22 with Business & Economics categories.


The index of an equilibrium in a game gives information about the "stability" of the equilibrium, for example with respect to game dynamics. Unfortunately, index theory is often very technical. This book presents a new geometric construction that visualises the index in an intuitive way. For example, a 3×n game, for any n, can be represented by a figure in the plane, from which one can read off any equilibrium, and its index as a geometric orientation. With this insight, the index can be characterised in strategic terms alone. Moreover, certain "hyperstable" equilibrium components are seen to have nonzero index. The construction gives an elementary proof that two-player games have a Nash equilibrium, and, in an unusual direction, the powerful fixed point theorem of Brouwer.



Algorithmic Game Theory


Algorithmic Game Theory
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Author : Noam Nisan
language : en
Publisher: Cambridge University Press
Release Date : 2007-09-24

Algorithmic Game Theory written by Noam Nisan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-24 with Computers categories.


In recent years game theory has had a substantial impact on computer science, especially on Internet- and e-commerce-related issues. Algorithmic Game Theory, first published in 2007, develops the central ideas and results of this exciting area in a clear and succinct manner. More than 40 of the top researchers in this field have written chapters that go from the foundations to the state of the art. Basic chapters on algorithmic methods for equilibria, mechanism design and combinatorial auctions are followed by chapters on important game theory applications such as incentives and pricing, cost sharing, information markets and cryptography and security. This definitive work will set the tone of research for the next few years and beyond. Students, researchers, and practitioners alike need to learn more about these fascinating theoretical developments and their widespread practical application.



A Geometric Combinatorial Approach To Index And Stability In Bimatrix Games


A Geometric Combinatorial Approach To Index And Stability In Bimatrix Games
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Author : Arndt Von Schemde
language : en
Publisher:
Release Date : 2004

A Geometric Combinatorial Approach To Index And Stability In Bimatrix Games written by Arndt Von Schemde and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.




Computational Aspects Of General Equilibrium Theory


Computational Aspects Of General Equilibrium Theory
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Author : Donald Brown
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-08

Computational Aspects Of General Equilibrium Theory written by Donald Brown and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-08 with Business & Economics categories.


This monograph presents a general equilibrium methodology for microeconomic policy analysis. It is intended to serve as an alternative to the now classical, axiomatic general equilibrium theory as exposited in Debreu`s Theory of Value (1959) or Arrow and Hahn`s General Competitive Analysis (1971). The monograph consists of several essays written over the last decade. It also contains an appendix by Charles Steinhorn on the elements of O-minimal structures.



Complex Systems Approach To Economic Dynamics


Complex Systems Approach To Economic Dynamics
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Author : Abraham C.-L. Chian
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-13

Complex Systems Approach To Economic Dynamics written by Abraham C.-L. Chian and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-13 with Business & Economics categories.


Economic Systems exhibit complex dynamics evidenced by large-amplitude and aperiodic fluctuations in economic variables, such as foreign exchange rates and stock market prices, indicating that these systems are driven far from the equilibrium. Characterization of the complex behavior of economic cycles, by identifying regular and irregular patterns and regime switching in economic time series, is the key for pattern recognition and forecasting of economic cycles. Statistical analysis of stock markets and foreign exchange markets has demonstrated the intermittent nature of economic time series. A nonlinear model of business cycles is able to simulate intermittency arising from order-chaos and chaos-chaos transitions. This monograph introduces new concepts of unstable periodic orbits and chaotic saddles which are unstable structures embedded in a chaotic attractor, responsible for economic intermittency.



Algorithmic Game Theory


Algorithmic Game Theory
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Author : Burkhard Monien
language : en
Publisher: Springer
Release Date : 2008-04-20

Algorithmic Game Theory written by Burkhard Monien and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-20 with Computers categories.


This book constitutes the proceedings of the First International Symposium on Algorithmic Game Theory. It covers routing and scheduling, markets, mechanism design, a potpourri of games, solution concepts, and cost sharing.



The Stability Concept Of Evolutionary Game Theory


The Stability Concept Of Evolutionary Game Theory
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Author : Ross Cressman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

The Stability Concept Of Evolutionary Game Theory written by Ross Cressman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.


These Notes grew from my research in evolutionary biology, specifically on the theory of evolutionarily stable strategies (ESS theory), over the past ten years. Personally, evolutionary game theory has given me the opportunity to transfer my enthusiasm for abstract mathematics to more practical pursuits. I was fortunate to have entered this field in its infancy when many biologists recognized its potential but were not prepared to grant it general acceptance. This is no longer the case. ESS theory is now a rapidly expanding (in both applied and theoretical directions) force that no evolutionary biologist can afford to ignore. Perhaps, to continue the life-cycle metaphor, ESS theory is now in its late adolescence and displays much of the optimism and exuberance of this exciting age. There are dangers in writing a text about a theory at this stage of development. A comprehensive treatment would involve too many loose ends for the reader to appreciate the central message. On the other hand, the current central message may soon become obsolete as the theory matures. Although the restricted topics I have chosen for this text reflect my own research bias, I am confident they will remain the theoretical basis of ESS theory. Indeed, I feel the adult maturity of ESS theory is close at hand and I hope the text will play an important role in this achievement.



The Knowledge Ahead Approach To Risk


The Knowledge Ahead Approach To Risk
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Author : Robin Pope
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-11-23

The Knowledge Ahead Approach To Risk written by Robin Pope and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-23 with Business & Economics categories.


This book is written for those seeking a decision theory appropriate for use in serious choices such as insurance. It employs stages of knowledge ahead to track satisfactions and dissatisfactions. From experimental and questionnaire data, people take into account such stages of knowledge ahead satisfactions and dissatisfactions. This means we must go beyond standard decision theories like expected utility or cumulative prospect theory.



Game Theoretical Foundations Of Evolutionary Stability


Game Theoretical Foundations Of Evolutionary Stability
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Author : Immanuel M. Bomze
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-19

Game Theoretical Foundations Of Evolutionary Stability written by Immanuel M. Bomze and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-19 with Business & Economics categories.


These Lecture Notes arose from discussions we had over a working paper written by the first author in fall 1987. We decided then to write a short paper about the basic structure of evolutionary stability and found ourselves ending up with a book manuscript. Parts of the material contained herein were presented in a seminar at the Department of Mathematics at the University of Vienna, as well as at a workshop on evolutionary game theory in Bielefeld. The final version of the manuscript has certainly benefitted from critical comments and suggestions by the participants of both the seminar and the workshop. Thanks are also due to S. Bomze-de Barba, R. Burger, G. Danninger, J. Hofbauer, R. Selten, K. Sigmund, G. Stiastny and F. Weising. The co-operation of W. Muller from Springer Verlag, Heidelberg, is gratefully acknowledged. Vienna, November 1988 Immanuel M. Bomze Benedikt M. Potscher III Contents 1. Introduction 1 2. Strategies and payoffs 5 2. 1. A general setting for evolutionary game theory 6 2. 2. Mixed strategies and population games 8 2. 3. Finite number of strategies . . . . . 13 2. 4. Infinitely many (pure) strategies 15 2. 5. Structured populations: asymmetric contests and multitype games 17 2. 6. Additional remarks . . . . . . . . . . . . . . . . . . . . . 21 3. Evolutionary stability 25 3. 1. Definition of evolutionary stability 25 3. 2. Evolutionary stability and solution concepts in classical game theory 30 3. 3. Conditions for evolutionary stability based on the normal cone 31 3. 4.